The gauge cell Monte Carlo method [Neimark and Vishnyakov, J. Chem. Phys. 122, 234108 (2005)] for calculations of chemical potential in dense and strongly inhomogeneous fluids is extended to multicomponent systems. The system of interest is simulated in a sample cell that is placed in chemical contact with several gauge cells of limited capacity, one gauge cell per component. Thus, each component can be exchanged between the sample cell and the respective gauge cell. The sample and gauge cells are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of concentration fluctuations for the respective component in the sample cell. The chemical potentials are rigorously calculated from the equilibrium distribution of particles between the system and the gauges, and the results do not depend on the gauge size. For large systems, the chemical potentials can be accurately estimated from the average densities in the gauge cells. The proposed method was tested against the literature data on the vapor-liquid equilibrium in a binary mixture of subcritical and supercritical fluids and against the grand canonical and Widom insertion Monte Carlo methods for a binary mixture confined to a very narrow spherical pore. The method is specifically suitable for simulations of metastable and labile states in multicomponent confined fluids.